with the \(p\) -norm defined as \(\Vert  \mathbf {u} \Vert _p = \@root p \of { \sum _{i=1}^n |u_i|^p}\) . A vector \(\mathbf {v} \in \mathbb {R}^n\)  is an eigenvector of \(\Delta _p\)  if and only if it is a critical point of (REF ) [1]}. The associated \(p\) -eigenvalue is given by \(F_p(\mathbf {v}) = \lambda _p\) . The functional \(F_p\)  is nonconvex, and it is easy to notice that for some scalar \(\gamma \in \mathbb {R}\)  it is invariant under scaling, and thus \(F_p(\gamma \mathbf {u}) = F_p(\mathbf {u})\) .
